Question 87
Let $A$, $B$, $C$, $P$ and $Q$ be five pairwise different points in the plane. Suppose that $A$, $B$ and $C$ are not collinear and that
$$
\frac{AP}{BP} = \frac{AQ}{BQ} = \frac{21}{20},
$$
$$
\frac{BP}{CP} = \frac{BQ}{CQ} = \frac{20}{19}.
$$
Prove that the line $PQ$ contains the circumcentre of the triangle $ABC$.
$$
\frac{AP}{BP} = \frac{AQ}{BQ} = \frac{21}{20},
$$
$$
\frac{BP}{CP} = \frac{BQ}{CQ} = \frac{20}{19}.
$$
Prove that the line $PQ$ contains the circumcentre of the triangle $ABC$.